Gorenstein injective and projective complexes
Gorenstein injective and projective complexes
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DOI：
10.1080/00927879808826229
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发表时间：
1998
影响因子：
0.7
通讯作者：
E. Enochs;J. R. G. Rozas
中科院分区：
文献类型：
--
作者：
E. Enochs;J. R. G. Rozas
本文将Gorenstein内射模和射影模的概念推广到配合物的概念，并对这种配合物进行了刻画。证明了在n-Gorenstein环上，每个配合物都有一个Gorenstein注入包络，并且证明了每个这样的包络都是一个拟同构。当环是交换的、局部的和Gorenstein的，Auslander宣布每个有限生成的r模都有一个有限生成的Gorenstein投影盖。我们证明了在这样一个环上所有项有限生成的有界复合体都有一个Gorenstein投影盖，并且证明了这些盖是拟同构的。
In this article we extend the notion of Gorenstein injective and projective modules to that of complexes and characterize such complexes. We prove that over an n-Gorenstein ring every complex has a Gorenstein injective envelope and we show that every such envelope is a quasi-isomorphim.. When the ring is commutative, local and Gorenstein, Auslander announced that every finitely generated R-module has a finitely generated Gorenstein projective cover. We show that every bounded above complex having all terms finitely generated over such a ring has a Gorenstein projective cover and we show that these covers are quasi-isomorphisms.